{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Random Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Random signals are signals whose values are not (or only to a limited extend) predictable. Frequently used alternative terms are\n",
    "\n",
    "* stochastic signals\n",
    "* non-deterministic signals\n",
    "\n",
    "Random signals play an important role in various fields of signal processing and communications. This is due to the fact that only random signals carry information. A signal which is observed by a receiver has to be unknown to some degree in order to represent novel [information](https://en.wikipedia.org/wiki/Information).\n",
    "\n",
    "Random signals are often classified as useful/desired and disturbing/interfering signals. For instance\n",
    "\n",
    "* useful signals: data, speech, music, images, ...\n",
    "* disturbing signals: thermal noise at a resistor, amplifier noise, quantization noise, cosmic microwave background...\n",
    "\n",
    "Practical signals are frequently modeled as a combination of useful signals and additive noise.\n",
    "\n",
    "As the values of a random signal cannot be foreseen, the properties of random signals are described by the their statistical characteristics. One measure is for instance the average value of a random signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Random Signals**\n",
    "\n",
    "The following audio examples illustrate the characteristics of some deterministic and random signals. Lower the volume of your headphones or loudspeakers before playing back the examples.\n",
    "\n",
    "1. Cosine signal\n",
    "\n",
    "    <audio src=\"./cosine.wav\" controls>Your browser does not support the audio element.</audio>[./cosine.wav](./cosine.wav)\n",
    "2. Noise\n",
    "\n",
    "    <audio src=\"./noise.wav\" controls>Your browser does not support the audio element.</audio>[./noise.wav](./noise.wav)\n",
    "3. Cosine signal superpositioned by noise\n",
    "\n",
    "    <audio src=\"./cosine_noise.wav\" controls>Your browser does not support the audio element.</audio>[./cosine_noise.wav](./cosine_noise.wav)\n",
    "4. Speech signal\n",
    "\n",
    "    <audio src=\"../data/speech.wav\" controls>Your browser does not support the audio element.</audio>[../data/speech.wav](../data/speech.wav)\n",
    "5. Speech signal superpositioned by noise\n",
    "\n",
    "    <audio src=\"./speech_noise.wav\" controls>Your browser does not support the audio element.</audio>[./speech_noise.wav](./speech_noise.wav)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Excercise**\n",
    "\n",
    "* Which example can be considered as deterministic, random signal or combination of both?\n",
    "\n",
    "Solution: The cosine signal is the only deterministic signal. Noise and speech are random signals, as their samples can not (or only to a limited extend) be predicted from previous samples. The superposition of the cosine and noise signals is a combination of a deterministic and a random signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Processing of Random Signals\n",
    "\n",
    "In contrary to the assumption of deterministic signals in traditional signal processing, [statistical signal processing](https://en.wikipedia.org/wiki/Statistical_signal_processing) treats signals explicitly as random signals. Two prominent application examples involving random signals are:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Measurement of physical quantities\n",
    "\n",
    "The measurement of physical quantities is often subject to additive noise and distortions. The additive noise models e.g. the sensor noise. The distortions, by e.g. the transmission properties of an amplifier, may be modeled by a system.\n",
    "\n",
    "![Model for the measurement of physical quantities](measurement_channel.png)\n",
    "\n",
    "$\\mathcal{H}$ denotes an arbitrary (not necessarily LTI) system. The aim of statistical signal processing is to estimate the physical quantity from the observed sensor data, given some knowledge on the disturbing system and the statistical properties of the noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Communication channel\n",
    "\n",
    "In communications engineering a message is sent over a channel that distorts the signal by e.g. multipath propagation. Additive noise is present at the receiver due to background and amplifier noise.\n",
    "\n",
    "![Model for the transmission of a message over a communication channel](communication_channel.png)\n",
    "\n",
    "The aim of statistical signal processing is to estimate the sent message from the received message, given some knowledge on the disturbing system and the statistical properties of the noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Processes\n",
    "\n",
    "A random process is a [stochastic process](https://en.wikipedia.org/wiki/Stochastic_process) which generates an ensemble of random signals. A random process\n",
    "\n",
    "* provides a mathematical model for an ensemble of random signals and\n",
    "* generates different sample functions with specific common properties.\n",
    "\n",
    "It is important to differentiate between an\n",
    "\n",
    "* *ensemble*: collection of all possible signals of a random process and an\n",
    "* *sample function*: one specific random signal.\n",
    "\n",
    "An example for a random process is speech produced by humans. Here the ensemble is composed from the speech signals produced by all humans on earth, one particular speech signal produced by one person at a specific time is a sample function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Sample functions of a random process**\n",
    "\n",
    "The following example shows sample functions of a continuous amplitude real-valued random process. All sample functions have the same properties with respect to certain statistical measures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": "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\n",
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"869.774375pt\" version=\"1.1\" viewBox=\"0 0 701.979688 869.774375\" width=\"701.979688pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 869.774375 \n",
       "L 701.979688 869.774375 \n",
       "L 701.979688 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 42.620313 137.458125 \n",
       "L 694.779688 137.458125 \n",
       "L 694.779688 22.318125 \n",
       "L 42.620313 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 62.382718 137.458125 \n",
       "L 62.382718 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_2\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"mb10eeb65be\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"62.382718\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(59.201468 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 161.194744 137.458125 \n",
       "L 161.194744 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"161.194744\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(158.013494 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 260.006771 137.458125 \n",
       "L 260.006771 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"260.006771\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 10 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(253.644271 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 358.818797 137.458125 \n",
       "L 358.818797 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"358.818797\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 15 -->\n",
       "      <g transform=\"translate(352.456297 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 457.630824 137.458125 \n",
       "L 457.630824 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"457.630824\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 20 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(451.268324 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 556.44285 137.458125 \n",
       "L 556.44285 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"556.44285\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 25 -->\n",
       "      <g transform=\"translate(550.08035 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 655.254877 137.458125 \n",
       "L 655.254877 22.318125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"655.254877\" xlink:href=\"#mb10eeb65be\" y=\"137.458125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 30 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(648.892377 152.056563)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_8\">\n",
       "     <!-- $k$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 18.3125 75.984375 \n",
       "L 27.296875 75.984375 \n",
       "L 18.703125 31.6875 \n",
       "L 49.515625 54.6875 \n",
       "L 61.1875 54.6875 \n",
       "L 26.8125 28.515625 \n",
       "L 51.90625 0 \n",
       "L 41.015625 0 \n",
       "L 17.671875 26.703125 \n",
       "L 12.5 0 \n",
       "L 3.515625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-Oblique-107\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(365.8 165.734688)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 42.620313 118.268125 \n",
       "L 694.779688 118.268125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m07f65042cd\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"118.268125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 122.067344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 42.620313 79.888125 \n",
       "L 694.779688 79.888125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"79.888125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257813 83.687344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <path clip-path=\"url(#p288a196540)\" d=\"M 42.620313 41.508125 \n",
       "L 694.779688 41.508125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"41.508125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(29.257813 45.307344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_12\">\n",
       "     <!-- $x_0[k]$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 60.015625 54.6875 \n",
       "L 34.90625 27.875 \n",
       "L 50.296875 0 \n",
       "L 39.984375 0 \n",
       "L 28.421875 21.6875 \n",
       "L 8.296875 0 \n",
       "L -2.59375 0 \n",
       "L 24.3125 28.8125 \n",
       "L 10.015625 54.6875 \n",
       "L 20.3125 54.6875 \n",
       "L 30.8125 34.90625 \n",
       "L 49.125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-Oblique-120\"/>\n",
       "      <path d=\"M 8.59375 75.984375 \n",
       "L 29.296875 75.984375 \n",
       "L 29.296875 69 \n",
       "L 17.578125 69 \n",
       "L 17.578125 -6.203125 \n",
       "L 29.296875 -6.203125 \n",
       "L 29.296875 -13.1875 \n",
       "L 8.59375 -13.1875 \n",
       "z\n",
       "\" id=\"DejaVuSans-91\"/>\n",
       "      <path d=\"M 30.421875 75.984375 \n",
       "L 30.421875 -13.1875 \n",
       "L 9.71875 -13.1875 \n",
       "L 9.71875 -6.203125 \n",
       "L 21.390625 -6.203125 \n",
       "L 21.390625 69 \n",
       "L 9.71875 69 \n",
       "L 9.71875 75.984375 \n",
       "z\n",
       "\" id=\"DejaVuSans-93\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(14.798438 92.038125)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(59.179688 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      <use transform=\"translate(106.450195 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(145.463867 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(203.374023 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\">\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 62.382718 79.888125 \n",
       "L 62.382718 46.03596 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 82.145123 79.888125 \n",
       "L 82.145123 72.209108 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 101.907528 79.888125 \n",
       "L 101.907528 61.106143 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 121.669934 79.888125 \n",
       "L 121.669934 36.885385 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 141.432339 79.888125 \n",
       "L 141.432339 44.049687 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 161.194744 79.888125 \n",
       "L 161.194744 98.642088 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 180.95715 79.888125 \n",
       "L 180.95715 61.655928 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 200.719555 79.888125 \n",
       "L 200.719555 82.79267 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 220.48196 79.888125 \n",
       "L 220.48196 81.868895 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 240.244366 79.888125 \n",
       "L 240.244366 72.00874 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 260.006771 79.888125 \n",
       "L 260.006771 77.123929 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 279.769176 79.888125 \n",
       "L 279.769176 51.980616 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 299.531581 79.888125 \n",
       "L 299.531581 65.283811 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 319.293987 79.888125 \n",
       "L 319.293987 77.553181 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 339.056392 79.888125 \n",
       "L 339.056392 71.37039 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 358.818797 79.888125 \n",
       "L 358.818797 73.484915 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 378.581203 79.888125 \n",
       "L 378.581203 51.216748 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 398.343608 79.888125 \n",
       "L 398.343608 83.825112 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 418.106013 79.888125 \n",
       "L 418.106013 73.880356 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 437.868419 79.888125 \n",
       "L 437.868419 96.278222 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 457.630824 79.888125 \n",
       "L 457.630824 128.88 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 477.393229 79.888125 \n",
       "L 477.393229 67.345184 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 497.155634 79.888125 \n",
       "L 497.155634 63.299594 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 516.91804 79.888125 \n",
       "L 516.91804 94.130272 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 536.680445 79.888125 \n",
       "L 536.680445 36.331534 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 556.44285 79.888125 \n",
       "L 556.44285 107.797402 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 576.205256 79.888125 \n",
       "L 576.205256 79.010019 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 595.967661 79.888125 \n",
       "L 595.967661 83.480183 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 615.730066 79.888125 \n",
       "L 615.730066 50.474092 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 635.492472 79.888125 \n",
       "L 635.492472 51.69113 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 655.254877 79.888125 \n",
       "L 655.254877 76.914684 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 675.017282 79.888125 \n",
       "L 675.017282 72.631186 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_21\">\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m901aa5411f\" style=\"stroke:#1f77b4;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p288a196540)\">\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"62.382718\" xlink:href=\"#m901aa5411f\" y=\"46.03596\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"82.145123\" xlink:href=\"#m901aa5411f\" y=\"72.209108\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"101.907528\" xlink:href=\"#m901aa5411f\" y=\"61.106143\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"121.669934\" xlink:href=\"#m901aa5411f\" y=\"36.885385\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"141.432339\" xlink:href=\"#m901aa5411f\" y=\"44.049687\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"161.194744\" xlink:href=\"#m901aa5411f\" y=\"98.642088\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"180.95715\" xlink:href=\"#m901aa5411f\" y=\"61.655928\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"200.719555\" xlink:href=\"#m901aa5411f\" y=\"82.79267\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"220.48196\" xlink:href=\"#m901aa5411f\" y=\"81.868895\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"240.244366\" xlink:href=\"#m901aa5411f\" y=\"72.00874\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"260.006771\" xlink:href=\"#m901aa5411f\" y=\"77.123929\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"279.769176\" xlink:href=\"#m901aa5411f\" y=\"51.980616\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"299.531581\" xlink:href=\"#m901aa5411f\" y=\"65.283811\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"319.293987\" xlink:href=\"#m901aa5411f\" y=\"77.553181\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"339.056392\" xlink:href=\"#m901aa5411f\" y=\"71.37039\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"358.818797\" xlink:href=\"#m901aa5411f\" y=\"73.484915\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"378.581203\" xlink:href=\"#m901aa5411f\" y=\"51.216748\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"398.343608\" xlink:href=\"#m901aa5411f\" y=\"83.825112\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"418.106013\" xlink:href=\"#m901aa5411f\" y=\"73.880356\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"437.868419\" xlink:href=\"#m901aa5411f\" y=\"96.278222\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"457.630824\" xlink:href=\"#m901aa5411f\" y=\"128.88\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"477.393229\" xlink:href=\"#m901aa5411f\" y=\"67.345184\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"497.155634\" xlink:href=\"#m901aa5411f\" y=\"63.299594\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"516.91804\" xlink:href=\"#m901aa5411f\" y=\"94.130272\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"536.680445\" xlink:href=\"#m901aa5411f\" y=\"36.331534\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"556.44285\" xlink:href=\"#m901aa5411f\" y=\"107.797402\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"576.205256\" xlink:href=\"#m901aa5411f\" y=\"79.010019\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"595.967661\" xlink:href=\"#m901aa5411f\" y=\"83.480183\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"615.730066\" xlink:href=\"#m901aa5411f\" y=\"50.474092\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"635.492472\" xlink:href=\"#m901aa5411f\" y=\"51.69113\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"655.254877\" xlink:href=\"#m901aa5411f\" y=\"76.914684\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"675.017282\" xlink:href=\"#m901aa5411f\" y=\"72.631186\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_22\">\n",
       "    <path clip-path=\"url(#p288a196540)\" d=\"M 62.382718 79.888125 \n",
       "L 675.017282 79.888125 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 42.620313 137.458125 \n",
       "L 42.620313 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 694.779688 137.458125 \n",
       "L 694.779688 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 42.620313 137.458125 \n",
       "L 694.779688 137.458125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 42.620313 22.318125 \n",
       "L 694.779688 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_13\">\n",
       "    <!-- Sample Function 0 -->\n",
       "    <defs>\n",
       "     <path d=\"M 53.515625 70.515625 \n",
       "L 53.515625 60.890625 \n",
       "Q 47.90625 63.578125 42.921875 64.890625 \n",
       "Q 37.9375 66.21875 33.296875 66.21875 \n",
       "Q 25.25 66.21875 20.875 63.09375 \n",
       "Q 16.5 59.96875 16.5 54.203125 \n",
       "Q 16.5 49.359375 19.40625 46.890625 \n",
       "Q 22.3125 44.4375 30.421875 42.921875 \n",
       "L 36.375 41.703125 \n",
       "Q 47.40625 39.59375 52.65625 34.296875 \n",
       "Q 57.90625 29 57.90625 20.125 \n",
       "Q 57.90625 9.515625 50.796875 4.046875 \n",
       "Q 43.703125 -1.421875 29.984375 -1.421875 \n",
       "Q 24.8125 -1.421875 18.96875 -0.25 \n",
       "Q 13.140625 0.921875 6.890625 3.21875 \n",
       "L 6.890625 13.375 \n",
       "Q 12.890625 10.015625 18.65625 8.296875 \n",
       "Q 24.421875 6.59375 29.984375 6.59375 \n",
       "Q 38.421875 6.59375 43.015625 9.90625 \n",
       "Q 47.609375 13.234375 47.609375 19.390625 \n",
       "Q 47.609375 24.75 44.3125 27.78125 \n",
       "Q 41.015625 30.8125 33.5 32.328125 \n",
       "L 27.484375 33.5 \n",
       "Q 16.453125 35.6875 11.515625 40.375 \n",
       "Q 6.59375 45.0625 6.59375 53.421875 \n",
       "Q 6.59375 63.09375 13.40625 68.65625 \n",
       "Q 20.21875 74.21875 32.171875 74.21875 \n",
       "Q 37.3125 74.21875 42.625 73.28125 \n",
       "Q 47.953125 72.359375 53.515625 70.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-83\"/>\n",
       "     <path d=\"M 34.28125 27.484375 \n",
       "Q 23.390625 27.484375 19.1875 25 \n",
       "Q 14.984375 22.515625 14.984375 16.5 \n",
       "Q 14.984375 11.71875 18.140625 8.90625 \n",
       "Q 21.296875 6.109375 26.703125 6.109375 \n",
       "Q 34.1875 6.109375 38.703125 11.40625 \n",
       "Q 43.21875 16.703125 43.21875 25.484375 \n",
       "L 43.21875 27.484375 \n",
       "z\n",
       "M 52.203125 31.203125 \n",
       "L 52.203125 0 \n",
       "L 43.21875 0 \n",
       "L 43.21875 8.296875 \n",
       "Q 40.140625 3.328125 35.546875 0.953125 \n",
       "Q 30.953125 -1.421875 24.3125 -1.421875 \n",
       "Q 15.921875 -1.421875 10.953125 3.296875 \n",
       "Q 6 8.015625 6 15.921875 \n",
       "Q 6 25.140625 12.171875 29.828125 \n",
       "Q 18.359375 34.515625 30.609375 34.515625 \n",
       "L 43.21875 34.515625 \n",
       "L 43.21875 35.40625 \n",
       "Q 43.21875 41.609375 39.140625 45 \n",
       "Q 35.0625 48.390625 27.6875 48.390625 \n",
       "Q 23 48.390625 18.546875 47.265625 \n",
       "Q 14.109375 46.140625 10.015625 43.890625 \n",
       "L 10.015625 52.203125 \n",
       "Q 14.9375 54.109375 19.578125 55.046875 \n",
       "Q 24.21875 56 28.609375 56 \n",
       "Q 40.484375 56 46.34375 49.84375 \n",
       "Q 52.203125 43.703125 52.203125 31.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-97\"/>\n",
       "     <path d=\"M 52 44.1875 \n",
       "Q 55.375 50.25 60.0625 53.125 \n",
       "Q 64.75 56 71.09375 56 \n",
       "Q 79.640625 56 84.28125 50.015625 \n",
       "Q 88.921875 44.046875 88.921875 33.015625 \n",
       "L 88.921875 0 \n",
       "L 79.890625 0 \n",
       "L 79.890625 32.71875 \n",
       "Q 79.890625 40.578125 77.09375 44.375 \n",
       "Q 74.3125 48.1875 68.609375 48.1875 \n",
       "Q 61.625 48.1875 57.5625 43.546875 \n",
       "Q 53.515625 38.921875 53.515625 30.90625 \n",
       "L 53.515625 0 \n",
       "L 44.484375 0 \n",
       "L 44.484375 32.71875 \n",
       "Q 44.484375 40.625 41.703125 44.40625 \n",
       "Q 38.921875 48.1875 33.109375 48.1875 \n",
       "Q 26.21875 48.1875 22.15625 43.53125 \n",
       "Q 18.109375 38.875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.1875 51.21875 25.484375 53.609375 \n",
       "Q 29.78125 56 35.6875 56 \n",
       "Q 41.65625 56 45.828125 52.96875 \n",
       "Q 50 49.953125 52 44.1875 \n",
       "z\n",
       "\" id=\"DejaVuSans-109\"/>\n",
       "     <path d=\"M 18.109375 8.203125 \n",
       "L 18.109375 -20.796875 \n",
       "L 9.078125 -20.796875 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "z\n",
       "M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-112\"/>\n",
       "     <path d=\"M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-108\"/>\n",
       "     <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "     <path id=\"DejaVuSans-32\"/>\n",
       "     <path d=\"M 9.8125 72.90625 \n",
       "L 51.703125 72.90625 \n",
       "L 51.703125 64.59375 \n",
       "L 19.671875 64.59375 \n",
       "L 19.671875 43.109375 \n",
       "L 48.578125 43.109375 \n",
       "L 48.578125 34.8125 \n",
       "L 19.671875 34.8125 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-70\"/>\n",
       "     <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "     <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "     <path d=\"M 48.78125 52.59375 \n",
       "L 48.78125 44.1875 \n",
       "Q 44.96875 46.296875 41.140625 47.34375 \n",
       "Q 37.3125 48.390625 33.40625 48.390625 \n",
       "Q 24.65625 48.390625 19.8125 42.84375 \n",
       "Q 14.984375 37.3125 14.984375 27.296875 \n",
       "Q 14.984375 17.28125 19.8125 11.734375 \n",
       "Q 24.65625 6.203125 33.40625 6.203125 \n",
       "Q 37.3125 6.203125 41.140625 7.25 \n",
       "Q 44.96875 8.296875 48.78125 10.40625 \n",
       "L 48.78125 2.09375 \n",
       "Q 45.015625 0.34375 40.984375 -0.53125 \n",
       "Q 36.96875 -1.421875 32.421875 -1.421875 \n",
       "Q 20.0625 -1.421875 12.78125 6.34375 \n",
       "Q 5.515625 14.109375 5.515625 27.296875 \n",
       "Q 5.515625 40.671875 12.859375 48.328125 \n",
       "Q 20.21875 56 33.015625 56 \n",
       "Q 37.15625 56 41.109375 55.140625 \n",
       "Q 45.0625 54.296875 48.78125 52.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-99\"/>\n",
       "     <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "     <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "     <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "    </defs>\n",
       "    <g transform=\"translate(312.7275 16.318125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-83\"/>\n",
       "     <use x=\"63.476562\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"124.755859\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "     <use x=\"222.167969\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "     <use x=\"285.644531\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "     <use x=\"313.427734\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"374.951172\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"406.738281\" xlink:href=\"#DejaVuSans-70\"/>\n",
       "     <use x=\"464.179688\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "     <use x=\"527.558594\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"590.9375\" xlink:href=\"#DejaVuSans-99\"/>\n",
       "     <use x=\"645.917969\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"685.126953\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"712.910156\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"774.091797\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"837.470703\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"869.257812\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"M 42.620313 311.148125 \n",
       "L 694.779688 311.148125 \n",
       "L 694.779688 196.008125 \n",
       "L 42.620313 196.008125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 62.382718 311.148125 \n",
       "L 62.382718 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"62.382718\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(59.201468 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 161.194744 311.148125 \n",
       "L 161.194744 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"161.194744\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(158.013494 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 260.006771 311.148125 \n",
       "L 260.006771 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"260.006771\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(253.644271 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 358.818797 311.148125 \n",
       "L 358.818797 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"358.818797\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- 15 -->\n",
       "      <g transform=\"translate(352.456297 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 457.630824 311.148125 \n",
       "L 457.630824 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"457.630824\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_18\">\n",
       "      <!-- 20 -->\n",
       "      <g transform=\"translate(451.268324 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 556.44285 311.148125 \n",
       "L 556.44285 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"556.44285\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 25 -->\n",
       "      <g transform=\"translate(550.08035 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 655.254877 311.148125 \n",
       "L 655.254877 196.008125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"655.254877\" xlink:href=\"#mb10eeb65be\" y=\"311.148125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 30 -->\n",
       "      <g transform=\"translate(648.892377 325.746562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_21\">\n",
       "     <!-- $k$ -->\n",
       "     <g transform=\"translate(365.8 339.424688)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_4\">\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 42.620313 291.958125 \n",
       "L 694.779688 291.958125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"291.958125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 295.757344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_39\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 42.620313 253.578125 \n",
       "L 694.779688 253.578125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_40\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"253.578125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257813 257.377344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_41\">\n",
       "      <path clip-path=\"url(#pfdf341ae17)\" d=\"M 42.620313 215.198125 \n",
       "L 694.779688 215.198125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_42\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"215.198125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(29.257813 218.997344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_25\">\n",
       "     <!-- $x_1[k]$ -->\n",
       "     <g transform=\"translate(14.798438 265.728125)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(59.179688 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      <use transform=\"translate(106.450195 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(145.463867 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(203.374023 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 62.382718 253.578125 \n",
       "L 62.382718 270.614733 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 82.145123 253.578125 \n",
       "L 82.145123 291.589609 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 101.907528 253.578125 \n",
       "L 101.907528 260.254559 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 121.669934 253.578125 \n",
       "L 121.669934 250.577788 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 141.432339 253.578125 \n",
       "L 141.432339 229.968847 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 161.194744 253.578125 \n",
       "L 161.194744 230.504456 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 180.95715 253.578125 \n",
       "L 180.95715 261.010927 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 200.719555 253.578125 \n",
       "L 200.719555 259.379315 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 220.48196 253.578125 \n",
       "L 220.48196 273.699856 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 240.244366 253.578125 \n",
       "L 240.244366 280.828269 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 260.006771 253.578125 \n",
       "L 260.006771 286.32145 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 279.769176 253.578125 \n",
       "L 279.769176 216.142745 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 299.531581 253.578125 \n",
       "L 299.531581 263.35835 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 319.293987 253.578125 \n",
       "L 319.293987 261.984771 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 339.056392 253.578125 \n",
       "L 339.056392 277.619268 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 358.818797 253.578125 \n",
       "L 358.818797 238.658085 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 378.581203 253.578125 \n",
       "L 378.581203 284.548825 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 398.343608 253.578125 \n",
       "L 398.343608 257.660611 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 418.106013 253.578125 \n",
       "L 418.106013 270.762128 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 437.868419 253.578125 \n",
       "L 437.868419 246.153466 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 457.630824 253.578125 \n",
       "L 457.630824 263.380476 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 477.393229 253.578125 \n",
       "L 477.393229 276.234457 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 497.155634 253.578125 \n",
       "L 497.155634 254.118942 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 516.91804 253.578125 \n",
       "L 516.91804 245.358436 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 536.680445 253.578125 \n",
       "L 536.680445 252.30166 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 556.44285 253.578125 \n",
       "L 556.44285 247.773689 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 576.205256 253.578125 \n",
       "L 576.205256 265.750766 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 595.967661 253.578125 \n",
       "L 595.967661 260.539128 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 615.730066 253.578125 \n",
       "L 615.730066 266.482641 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 635.492472 253.578125 \n",
       "L 635.492472 260.47795 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 655.254877 253.578125 \n",
       "L 655.254877 269.182402 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 675.017282 253.578125 \n",
       "L 675.017282 286.705488 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_43\">\n",
       "    <g clip-path=\"url(#pfdf341ae17)\">\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"62.382718\" xlink:href=\"#m901aa5411f\" y=\"270.614733\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"82.145123\" xlink:href=\"#m901aa5411f\" y=\"291.589609\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"101.907528\" xlink:href=\"#m901aa5411f\" y=\"260.254559\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"121.669934\" xlink:href=\"#m901aa5411f\" y=\"250.577788\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"141.432339\" xlink:href=\"#m901aa5411f\" y=\"229.968847\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"161.194744\" xlink:href=\"#m901aa5411f\" y=\"230.504456\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"180.95715\" xlink:href=\"#m901aa5411f\" y=\"261.010927\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"200.719555\" xlink:href=\"#m901aa5411f\" y=\"259.379315\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"220.48196\" xlink:href=\"#m901aa5411f\" y=\"273.699856\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"240.244366\" xlink:href=\"#m901aa5411f\" y=\"280.828269\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"260.006771\" xlink:href=\"#m901aa5411f\" y=\"286.32145\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"279.769176\" xlink:href=\"#m901aa5411f\" y=\"216.142745\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"299.531581\" xlink:href=\"#m901aa5411f\" y=\"263.35835\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"319.293987\" xlink:href=\"#m901aa5411f\" y=\"261.984771\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"339.056392\" xlink:href=\"#m901aa5411f\" y=\"277.619268\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"358.818797\" xlink:href=\"#m901aa5411f\" y=\"238.658085\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"378.581203\" xlink:href=\"#m901aa5411f\" y=\"284.548825\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"398.343608\" xlink:href=\"#m901aa5411f\" y=\"257.660611\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"418.106013\" xlink:href=\"#m901aa5411f\" y=\"270.762128\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"437.868419\" xlink:href=\"#m901aa5411f\" y=\"246.153466\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"457.630824\" xlink:href=\"#m901aa5411f\" y=\"263.380476\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"477.393229\" xlink:href=\"#m901aa5411f\" y=\"276.234457\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"497.155634\" xlink:href=\"#m901aa5411f\" y=\"254.118942\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"516.91804\" xlink:href=\"#m901aa5411f\" y=\"245.358436\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"536.680445\" xlink:href=\"#m901aa5411f\" y=\"252.30166\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"556.44285\" xlink:href=\"#m901aa5411f\" y=\"247.773689\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"576.205256\" xlink:href=\"#m901aa5411f\" y=\"265.750766\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"595.967661\" xlink:href=\"#m901aa5411f\" y=\"260.539128\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"615.730066\" xlink:href=\"#m901aa5411f\" y=\"266.482641\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"635.492472\" xlink:href=\"#m901aa5411f\" y=\"260.47795\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"655.254877\" xlink:href=\"#m901aa5411f\" y=\"269.182402\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"675.017282\" xlink:href=\"#m901aa5411f\" y=\"286.705488\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_44\">\n",
       "    <path clip-path=\"url(#pfdf341ae17)\" d=\"M 62.382718 253.578125 \n",
       "L 675.017282 253.578125 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"M 42.620313 311.148125 \n",
       "L 42.620313 196.008125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"M 694.779688 311.148125 \n",
       "L 694.779688 196.008125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"M 42.620313 311.148125 \n",
       "L 694.779688 311.148125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"M 42.620313 196.008125 \n",
       "L 694.779688 196.008125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_26\">\n",
       "    <!-- Sample Function 1 -->\n",
       "    <g transform=\"translate(312.7275 190.008125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-83\"/>\n",
       "     <use x=\"63.476562\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"124.755859\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "     <use x=\"222.167969\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "     <use x=\"285.644531\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "     <use x=\"313.427734\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"374.951172\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"406.738281\" xlink:href=\"#DejaVuSans-70\"/>\n",
       "     <use x=\"464.179688\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "     <use x=\"527.558594\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"590.9375\" xlink:href=\"#DejaVuSans-99\"/>\n",
       "     <use x=\"645.917969\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"685.126953\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"712.910156\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"774.091797\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"837.470703\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"869.257812\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_3\">\n",
       "   <g id=\"patch_12\">\n",
       "    <path d=\"M 42.620313 484.838125 \n",
       "L 694.779688 484.838125 \n",
       "L 694.779688 369.698125 \n",
       "L 42.620313 369.698125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_5\">\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_45\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 62.382718 484.838125 \n",
       "L 62.382718 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_46\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"62.382718\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_27\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(59.201468 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_47\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 161.194744 484.838125 \n",
       "L 161.194744 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_48\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"161.194744\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_28\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(158.013494 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_49\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 260.006771 484.838125 \n",
       "L 260.006771 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_50\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"260.006771\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(253.644271 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
       "     <g id=\"line2d_51\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 358.818797 484.838125 \n",
       "L 358.818797 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_52\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"358.818797\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- 15 -->\n",
       "      <g transform=\"translate(352.456297 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_19\">\n",
       "     <g id=\"line2d_53\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 457.630824 484.838125 \n",
       "L 457.630824 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_54\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"457.630824\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- 20 -->\n",
       "      <g transform=\"translate(451.268324 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_20\">\n",
       "     <g id=\"line2d_55\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 556.44285 484.838125 \n",
       "L 556.44285 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_56\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"556.44285\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_32\">\n",
       "      <!-- 25 -->\n",
       "      <g transform=\"translate(550.08035 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_21\">\n",
       "     <g id=\"line2d_57\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 655.254877 484.838125 \n",
       "L 655.254877 369.698125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_58\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"655.254877\" xlink:href=\"#mb10eeb65be\" y=\"484.838125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_33\">\n",
       "      <!-- 30 -->\n",
       "      <g transform=\"translate(648.892377 499.436562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_34\">\n",
       "     <!-- $k$ -->\n",
       "     <g transform=\"translate(365.8 513.114687)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_6\">\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_59\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 42.620313 465.648125 \n",
       "L 694.779688 465.648125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_60\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"465.648125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_35\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 469.447344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_61\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 42.620313 427.268125 \n",
       "L 694.779688 427.268125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_62\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"427.268125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_36\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257813 431.067344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_63\">\n",
       "      <path clip-path=\"url(#p23674a6dd6)\" d=\"M 42.620313 388.888125 \n",
       "L 694.779688 388.888125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_64\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"388.888125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_37\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(29.257813 392.687344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_38\">\n",
       "     <!-- $x_2[k]$ -->\n",
       "     <g transform=\"translate(14.798438 439.418125)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(59.179688 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      <use transform=\"translate(106.450195 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(145.463867 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(203.374023 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 62.382718 427.268125 \n",
       "L 62.382718 423.863317 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 82.145123 427.268125 \n",
       "L 82.145123 434.978301 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 101.907528 427.268125 \n",
       "L 101.907528 458.551631 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 121.669934 427.268125 \n",
       "L 121.669934 418.387334 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 141.432339 427.268125 \n",
       "L 141.432339 444.679181 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 161.194744 427.268125 \n",
       "L 161.194744 426.271293 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 180.95715 427.268125 \n",
       "L 180.95715 413.276877 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 200.719555 427.268125 \n",
       "L 200.719555 424.792943 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 220.48196 427.268125 \n",
       "L 220.48196 405.403026 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 240.244366 427.268125 \n",
       "L 240.244366 450.964432 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 260.006771 427.268125 \n",
       "L 260.006771 419.547189 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 279.769176 427.268125 \n",
       "L 279.769176 440.409631 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 299.531581 427.268125 \n",
       "L 299.531581 443.978722 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 319.293987 427.268125 \n",
       "L 319.293987 438.37625 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 339.056392 427.268125 \n",
       "L 339.056392 433.246818 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 358.818797 427.268125 \n",
       "L 358.818797 426.190312 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 378.581203 427.268125 \n",
       "L 378.581203 449.62735 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 398.343608 427.268125 \n",
       "L 398.343608 409.981265 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 418.106013 427.268125 \n",
       "L 418.106013 418.332063 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 437.868419 427.268125 \n",
       "L 437.868419 456.748641 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 457.630824 427.268125 \n",
       "L 457.630824 398.708565 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 477.393229 427.268125 \n",
       "L 477.393229 390.886012 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 497.155634 427.268125 \n",
       "L 497.155634 404.647345 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 516.91804 427.268125 \n",
       "L 516.91804 430.720883 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 536.680445 427.268125 \n",
       "L 536.680445 447.815868 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 556.44285 427.268125 \n",
       "L 556.44285 407.033196 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 576.205256 427.268125 \n",
       "L 576.205256 435.005091 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 595.967661 427.268125 \n",
       "L 595.967661 403.809404 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 615.730066 427.268125 \n",
       "L 615.730066 423.271328 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 635.492472 427.268125 \n",
       "L 635.492472 408.526422 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 655.254877 427.268125 \n",
       "L 655.254877 420.429454 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 675.017282 427.268125 \n",
       "L 675.017282 413.708986 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_65\">\n",
       "    <g clip-path=\"url(#p23674a6dd6)\">\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"62.382718\" xlink:href=\"#m901aa5411f\" y=\"423.863317\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"82.145123\" xlink:href=\"#m901aa5411f\" y=\"434.978301\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"101.907528\" xlink:href=\"#m901aa5411f\" y=\"458.551631\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"121.669934\" xlink:href=\"#m901aa5411f\" y=\"418.387334\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"141.432339\" xlink:href=\"#m901aa5411f\" y=\"444.679181\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"161.194744\" xlink:href=\"#m901aa5411f\" y=\"426.271293\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"180.95715\" xlink:href=\"#m901aa5411f\" y=\"413.276877\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"200.719555\" xlink:href=\"#m901aa5411f\" y=\"424.792943\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"220.48196\" xlink:href=\"#m901aa5411f\" y=\"405.403026\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"240.244366\" xlink:href=\"#m901aa5411f\" y=\"450.964432\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"260.006771\" xlink:href=\"#m901aa5411f\" y=\"419.547189\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"279.769176\" xlink:href=\"#m901aa5411f\" y=\"440.409631\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"299.531581\" xlink:href=\"#m901aa5411f\" y=\"443.978722\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"319.293987\" xlink:href=\"#m901aa5411f\" y=\"438.37625\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"339.056392\" xlink:href=\"#m901aa5411f\" y=\"433.246818\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"358.818797\" xlink:href=\"#m901aa5411f\" y=\"426.190312\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"378.581203\" xlink:href=\"#m901aa5411f\" y=\"449.62735\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"398.343608\" xlink:href=\"#m901aa5411f\" y=\"409.981265\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"418.106013\" xlink:href=\"#m901aa5411f\" y=\"418.332063\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"437.868419\" xlink:href=\"#m901aa5411f\" y=\"456.748641\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"457.630824\" xlink:href=\"#m901aa5411f\" y=\"398.708565\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"477.393229\" xlink:href=\"#m901aa5411f\" y=\"390.886012\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"497.155634\" xlink:href=\"#m901aa5411f\" y=\"404.647345\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"516.91804\" xlink:href=\"#m901aa5411f\" y=\"430.720883\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"536.680445\" xlink:href=\"#m901aa5411f\" y=\"447.815868\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"556.44285\" xlink:href=\"#m901aa5411f\" y=\"407.033196\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"576.205256\" xlink:href=\"#m901aa5411f\" y=\"435.005091\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"595.967661\" xlink:href=\"#m901aa5411f\" y=\"403.809404\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"615.730066\" xlink:href=\"#m901aa5411f\" y=\"423.271328\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"635.492472\" xlink:href=\"#m901aa5411f\" y=\"408.526422\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"655.254877\" xlink:href=\"#m901aa5411f\" y=\"420.429454\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"675.017282\" xlink:href=\"#m901aa5411f\" y=\"413.708986\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_66\">\n",
       "    <path clip-path=\"url(#p23674a6dd6)\" d=\"M 62.382718 427.268125 \n",
       "L 675.017282 427.268125 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_13\">\n",
       "    <path d=\"M 42.620313 484.838125 \n",
       "L 42.620313 369.698125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_14\">\n",
       "    <path d=\"M 694.779688 484.838125 \n",
       "L 694.779688 369.698125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_15\">\n",
       "    <path d=\"M 42.620313 484.838125 \n",
       "L 694.779688 484.838125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_16\">\n",
       "    <path d=\"M 42.620313 369.698125 \n",
       "L 694.779688 369.698125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_39\">\n",
       "    <!-- Sample Function 2 -->\n",
       "    <g transform=\"translate(312.7275 363.698125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-83\"/>\n",
       "     <use x=\"63.476562\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"124.755859\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "     <use x=\"222.167969\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "     <use x=\"285.644531\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "     <use x=\"313.427734\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"374.951172\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"406.738281\" xlink:href=\"#DejaVuSans-70\"/>\n",
       "     <use x=\"464.179688\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "     <use x=\"527.558594\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"590.9375\" xlink:href=\"#DejaVuSans-99\"/>\n",
       "     <use x=\"645.917969\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"685.126953\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"712.910156\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"774.091797\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"837.470703\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"869.257812\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_4\">\n",
       "   <g id=\"patch_17\">\n",
       "    <path d=\"M 42.620313 658.528125 \n",
       "L 694.779688 658.528125 \n",
       "L 694.779688 543.388125 \n",
       "L 42.620313 543.388125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_7\">\n",
       "    <g id=\"xtick_22\">\n",
       "     <g id=\"line2d_67\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 62.382718 658.528125 \n",
       "L 62.382718 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_68\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"62.382718\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_40\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(59.201468 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_23\">\n",
       "     <g id=\"line2d_69\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 161.194744 658.528125 \n",
       "L 161.194744 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_70\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"161.194744\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_41\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(158.013494 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_24\">\n",
       "     <g id=\"line2d_71\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 260.006771 658.528125 \n",
       "L 260.006771 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_72\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"260.006771\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_42\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(253.644271 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_25\">\n",
       "     <g id=\"line2d_73\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 358.818797 658.528125 \n",
       "L 358.818797 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_74\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"358.818797\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_43\">\n",
       "      <!-- 15 -->\n",
       "      <g transform=\"translate(352.456297 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_26\">\n",
       "     <g id=\"line2d_75\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 457.630824 658.528125 \n",
       "L 457.630824 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_76\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"457.630824\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_44\">\n",
       "      <!-- 20 -->\n",
       "      <g transform=\"translate(451.268324 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_27\">\n",
       "     <g id=\"line2d_77\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 556.44285 658.528125 \n",
       "L 556.44285 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_78\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"556.44285\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_45\">\n",
       "      <!-- 25 -->\n",
       "      <g transform=\"translate(550.08035 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_28\">\n",
       "     <g id=\"line2d_79\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 655.254877 658.528125 \n",
       "L 655.254877 543.388125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_80\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"655.254877\" xlink:href=\"#mb10eeb65be\" y=\"658.528125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_46\">\n",
       "      <!-- 30 -->\n",
       "      <g transform=\"translate(648.892377 673.126562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_47\">\n",
       "     <!-- $k$ -->\n",
       "     <g transform=\"translate(365.8 686.804687)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_8\">\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_81\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 42.620313 639.338125 \n",
       "L 694.779688 639.338125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_82\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"639.338125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_48\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 643.137344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_83\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 42.620313 600.958125 \n",
       "L 694.779688 600.958125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_84\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"600.958125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_49\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257813 604.757344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_85\">\n",
       "      <path clip-path=\"url(#p1fa8443931)\" d=\"M 42.620313 562.578125 \n",
       "L 694.779688 562.578125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_86\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"562.578125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_50\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(29.257813 566.377344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_51\">\n",
       "     <!-- $x_3[k]$ -->\n",
       "     <g transform=\"translate(14.798438 613.108125)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(59.179688 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      <use transform=\"translate(106.450195 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(145.463867 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(203.374023 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 62.382718 600.958125 \n",
       "L 62.382718 600.75663 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 82.145123 600.958125 \n",
       "L 82.145123 566.68727 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 101.907528 600.958125 \n",
       "L 101.907528 598.522682 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 121.669934 600.958125 \n",
       "L 121.669934 593.243949 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 141.432339 600.958125 \n",
       "L 141.432339 564.820463 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 161.194744 600.958125 \n",
       "L 161.194744 626.821621 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 180.95715 600.958125 \n",
       "L 180.95715 625.338732 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 200.719555 600.958125 \n",
       "L 200.719555 582.355402 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 220.48196 600.958125 \n",
       "L 220.48196 623.470363 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 240.244366 600.958125 \n",
       "L 240.244366 563.660034 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 260.006771 600.958125 \n",
       "L 260.006771 608.895473 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 279.769176 600.958125 \n",
       "L 279.769176 615.301783 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 299.531581 600.958125 \n",
       "L 299.531581 564.056868 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 319.293987 600.958125 \n",
       "L 319.293987 572.547046 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 339.056392 600.958125 \n",
       "L 339.056392 565.119669 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 358.818797 600.958125 \n",
       "L 358.818797 583.571128 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 378.581203 600.958125 \n",
       "L 378.581203 617.485046 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 398.343608 600.958125 \n",
       "L 398.343608 564.303979 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 418.106013 600.958125 \n",
       "L 418.106013 606.10111 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 437.868419 600.958125 \n",
       "L 437.868419 585.558987 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 457.630824 600.958125 \n",
       "L 457.630824 582.78036 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 477.393229 600.958125 \n",
       "L 477.393229 603.932769 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 497.155634 600.958125 \n",
       "L 497.155634 589.173942 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 516.91804 600.958125 \n",
       "L 516.91804 583.260979 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 536.680445 600.958125 \n",
       "L 536.680445 593.734519 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 556.44285 600.958125 \n",
       "L 556.44285 622.055626 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 576.205256 600.958125 \n",
       "L 576.205256 595.234934 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 595.967661 600.958125 \n",
       "L 595.967661 575.50478 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 615.730066 600.958125 \n",
       "L 615.730066 614.286882 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 635.492472 600.958125 \n",
       "L 635.492472 603.829612 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 655.254877 600.958125 \n",
       "L 655.254877 609.308722 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 675.017282 600.958125 \n",
       "L 675.017282 565.470754 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_87\">\n",
       "    <g clip-path=\"url(#p1fa8443931)\">\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"62.382718\" xlink:href=\"#m901aa5411f\" y=\"600.75663\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"82.145123\" xlink:href=\"#m901aa5411f\" y=\"566.68727\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"101.907528\" xlink:href=\"#m901aa5411f\" y=\"598.522682\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"121.669934\" xlink:href=\"#m901aa5411f\" y=\"593.243949\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"141.432339\" xlink:href=\"#m901aa5411f\" y=\"564.820463\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"161.194744\" xlink:href=\"#m901aa5411f\" y=\"626.821621\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"180.95715\" xlink:href=\"#m901aa5411f\" y=\"625.338732\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"200.719555\" xlink:href=\"#m901aa5411f\" y=\"582.355402\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"220.48196\" xlink:href=\"#m901aa5411f\" y=\"623.470363\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"240.244366\" xlink:href=\"#m901aa5411f\" y=\"563.660034\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"260.006771\" xlink:href=\"#m901aa5411f\" y=\"608.895473\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"279.769176\" xlink:href=\"#m901aa5411f\" y=\"615.301783\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"299.531581\" xlink:href=\"#m901aa5411f\" y=\"564.056868\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"319.293987\" xlink:href=\"#m901aa5411f\" y=\"572.547046\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"339.056392\" xlink:href=\"#m901aa5411f\" y=\"565.119669\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"358.818797\" xlink:href=\"#m901aa5411f\" y=\"583.571128\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"378.581203\" xlink:href=\"#m901aa5411f\" y=\"617.485046\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"398.343608\" xlink:href=\"#m901aa5411f\" y=\"564.303979\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"418.106013\" xlink:href=\"#m901aa5411f\" y=\"606.10111\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"437.868419\" xlink:href=\"#m901aa5411f\" y=\"585.558987\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"457.630824\" xlink:href=\"#m901aa5411f\" y=\"582.78036\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"477.393229\" xlink:href=\"#m901aa5411f\" y=\"603.932769\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"497.155634\" xlink:href=\"#m901aa5411f\" y=\"589.173942\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"516.91804\" xlink:href=\"#m901aa5411f\" y=\"583.260979\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"536.680445\" xlink:href=\"#m901aa5411f\" y=\"593.734519\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"556.44285\" xlink:href=\"#m901aa5411f\" y=\"622.055626\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"576.205256\" xlink:href=\"#m901aa5411f\" y=\"595.234934\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"595.967661\" xlink:href=\"#m901aa5411f\" y=\"575.50478\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"615.730066\" xlink:href=\"#m901aa5411f\" y=\"614.286882\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"635.492472\" xlink:href=\"#m901aa5411f\" y=\"603.829612\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"655.254877\" xlink:href=\"#m901aa5411f\" y=\"609.308722\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"675.017282\" xlink:href=\"#m901aa5411f\" y=\"565.470754\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_88\">\n",
       "    <path clip-path=\"url(#p1fa8443931)\" d=\"M 62.382718 600.958125 \n",
       "L 675.017282 600.958125 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_18\">\n",
       "    <path d=\"M 42.620313 658.528125 \n",
       "L 42.620313 543.388125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_19\">\n",
       "    <path d=\"M 694.779688 658.528125 \n",
       "L 694.779688 543.388125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_20\">\n",
       "    <path d=\"M 42.620313 658.528125 \n",
       "L 694.779688 658.528125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_21\">\n",
       "    <path d=\"M 42.620313 543.388125 \n",
       "L 694.779688 543.388125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_52\">\n",
       "    <!-- Sample Function 3 -->\n",
       "    <g transform=\"translate(312.7275 537.388125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-83\"/>\n",
       "     <use x=\"63.476562\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"124.755859\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "     <use x=\"222.167969\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "     <use x=\"285.644531\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "     <use x=\"313.427734\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"374.951172\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"406.738281\" xlink:href=\"#DejaVuSans-70\"/>\n",
       "     <use x=\"464.179688\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "     <use x=\"527.558594\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"590.9375\" xlink:href=\"#DejaVuSans-99\"/>\n",
       "     <use x=\"645.917969\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"685.126953\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"712.910156\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"774.091797\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"837.470703\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"869.257812\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_5\">\n",
       "   <g id=\"patch_22\">\n",
       "    <path d=\"M 42.620313 832.218125 \n",
       "L 694.779688 832.218125 \n",
       "L 694.779688 717.078125 \n",
       "L 42.620313 717.078125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_9\">\n",
       "    <g id=\"xtick_29\">\n",
       "     <g id=\"line2d_89\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 62.382718 832.218125 \n",
       "L 62.382718 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_90\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"62.382718\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_53\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(59.201468 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_30\">\n",
       "     <g id=\"line2d_91\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 161.194744 832.218125 \n",
       "L 161.194744 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_92\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"161.194744\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_54\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(158.013494 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_31\">\n",
       "     <g id=\"line2d_93\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 260.006771 832.218125 \n",
       "L 260.006771 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_94\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"260.006771\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_55\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(253.644271 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_32\">\n",
       "     <g id=\"line2d_95\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 358.818797 832.218125 \n",
       "L 358.818797 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_96\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"358.818797\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_56\">\n",
       "      <!-- 15 -->\n",
       "      <g transform=\"translate(352.456297 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_33\">\n",
       "     <g id=\"line2d_97\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 457.630824 832.218125 \n",
       "L 457.630824 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_98\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"457.630824\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_57\">\n",
       "      <!-- 20 -->\n",
       "      <g transform=\"translate(451.268324 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_34\">\n",
       "     <g id=\"line2d_99\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 556.44285 832.218125 \n",
       "L 556.44285 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_100\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"556.44285\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_58\">\n",
       "      <!-- 25 -->\n",
       "      <g transform=\"translate(550.08035 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_35\">\n",
       "     <g id=\"line2d_101\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 655.254877 832.218125 \n",
       "L 655.254877 717.078125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_102\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"655.254877\" xlink:href=\"#mb10eeb65be\" y=\"832.218125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_59\">\n",
       "      <!-- 30 -->\n",
       "      <g transform=\"translate(648.892377 846.816562)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_60\">\n",
       "     <!-- $k$ -->\n",
       "     <g transform=\"translate(365.8 860.494687)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_10\">\n",
       "    <g id=\"ytick_13\">\n",
       "     <g id=\"line2d_103\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 42.620313 813.028125 \n",
       "L 694.779688 813.028125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_104\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"813.028125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_61\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 816.827344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_14\">\n",
       "     <g id=\"line2d_105\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 42.620313 774.648125 \n",
       "L 694.779688 774.648125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_106\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"774.648125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_62\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257813 778.447344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_15\">\n",
       "     <g id=\"line2d_107\">\n",
       "      <path clip-path=\"url(#pbfebe2a693)\" d=\"M 42.620313 736.268125 \n",
       "L 694.779688 736.268125 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_108\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#m07f65042cd\" y=\"736.268125\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_63\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(29.257813 740.067344)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_64\">\n",
       "     <!-- $x_4[k]$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(14.798438 786.798125)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(59.179688 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      <use transform=\"translate(106.450195 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(145.463867 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(203.374023 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 62.382718 774.648125 \n",
       "L 62.382718 761.746789 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 82.145123 774.648125 \n",
       "L 82.145123 766.828932 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 101.907528 774.648125 \n",
       "L 101.907528 789.422814 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 121.669934 774.648125 \n",
       "L 121.669934 764.299933 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 141.432339 774.648125 \n",
       "L 141.432339 787.588569 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 161.194744 774.648125 \n",
       "L 161.194744 774.037297 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 180.95715 774.648125 \n",
       "L 180.95715 786.850011 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 200.719555 774.648125 \n",
       "L 200.719555 761.66737 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 220.48196 774.648125 \n",
       "L 220.48196 763.583347 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 240.244366 774.648125 \n",
       "L 240.244366 778.645378 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 260.006771 774.648125 \n",
       "L 260.006771 767.048756 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 279.769176 774.648125 \n",
       "L 279.769176 795.623975 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 299.531581 774.648125 \n",
       "L 299.531581 803.265358 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 319.293987 774.648125 \n",
       "L 319.293987 766.216198 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 339.056392 774.648125 \n",
       "L 339.056392 771.449661 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 358.818797 774.648125 \n",
       "L 358.818797 762.461872 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 378.581203 774.648125 \n",
       "L 378.581203 728.915577 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 398.343608 774.648125 \n",
       "L 398.343608 756.523564 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 418.106013 774.648125 \n",
       "L 418.106013 792.165184 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 437.868419 774.648125 \n",
       "L 437.868419 753.212582 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 457.630824 774.648125 \n",
       "L 457.630824 799.900388 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 477.393229 774.648125 \n",
       "L 477.393229 783.505934 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 497.155634 774.648125 \n",
       "L 497.155634 775.957681 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 516.91804 774.648125 \n",
       "L 516.91804 741.769078 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 536.680445 774.648125 \n",
       "L 536.680445 788.93997 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 556.44285 774.648125 \n",
       "L 556.44285 790.507481 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 576.205256 774.648125 \n",
       "L 576.205256 776.537429 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 595.967661 774.648125 \n",
       "L 595.967661 787.380273 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 615.730066 774.648125 \n",
       "L 615.730066 753.027982 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 635.492472 774.648125 \n",
       "L 635.492472 795.372011 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 655.254877 774.648125 \n",
       "L 655.254877 796.668048 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 675.017282 774.648125 \n",
       "L 675.017282 783.049892 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_109\">\n",
       "    <g clip-path=\"url(#pbfebe2a693)\">\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"62.382718\" xlink:href=\"#m901aa5411f\" y=\"761.746789\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"82.145123\" xlink:href=\"#m901aa5411f\" y=\"766.828932\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"101.907528\" xlink:href=\"#m901aa5411f\" y=\"789.422814\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"121.669934\" xlink:href=\"#m901aa5411f\" y=\"764.299933\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"141.432339\" xlink:href=\"#m901aa5411f\" y=\"787.588569\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"161.194744\" xlink:href=\"#m901aa5411f\" y=\"774.037297\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"180.95715\" xlink:href=\"#m901aa5411f\" y=\"786.850011\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"200.719555\" xlink:href=\"#m901aa5411f\" y=\"761.66737\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"220.48196\" xlink:href=\"#m901aa5411f\" y=\"763.583347\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"240.244366\" xlink:href=\"#m901aa5411f\" y=\"778.645378\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"260.006771\" xlink:href=\"#m901aa5411f\" y=\"767.048756\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"279.769176\" xlink:href=\"#m901aa5411f\" y=\"795.623975\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"299.531581\" xlink:href=\"#m901aa5411f\" y=\"803.265358\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"319.293987\" xlink:href=\"#m901aa5411f\" y=\"766.216198\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"339.056392\" xlink:href=\"#m901aa5411f\" y=\"771.449661\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"358.818797\" xlink:href=\"#m901aa5411f\" y=\"762.461872\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"378.581203\" xlink:href=\"#m901aa5411f\" y=\"728.915577\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"398.343608\" xlink:href=\"#m901aa5411f\" y=\"756.523564\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"418.106013\" xlink:href=\"#m901aa5411f\" y=\"792.165184\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"437.868419\" xlink:href=\"#m901aa5411f\" y=\"753.212582\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"457.630824\" xlink:href=\"#m901aa5411f\" y=\"799.900388\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"477.393229\" xlink:href=\"#m901aa5411f\" y=\"783.505934\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"497.155634\" xlink:href=\"#m901aa5411f\" y=\"775.957681\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"516.91804\" xlink:href=\"#m901aa5411f\" y=\"741.769078\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"536.680445\" xlink:href=\"#m901aa5411f\" y=\"788.93997\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"556.44285\" xlink:href=\"#m901aa5411f\" y=\"790.507481\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"576.205256\" xlink:href=\"#m901aa5411f\" y=\"776.537429\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"595.967661\" xlink:href=\"#m901aa5411f\" y=\"787.380273\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"615.730066\" xlink:href=\"#m901aa5411f\" y=\"753.027982\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"635.492472\" xlink:href=\"#m901aa5411f\" y=\"795.372011\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"655.254877\" xlink:href=\"#m901aa5411f\" y=\"796.668048\"/>\n",
       "     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"675.017282\" xlink:href=\"#m901aa5411f\" y=\"783.049892\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_110\">\n",
       "    <path clip-path=\"url(#pbfebe2a693)\" d=\"M 62.382718 774.648125 \n",
       "L 675.017282 774.648125 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-dasharray:1.5,2.475;stroke-dashoffset:0;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_23\">\n",
       "    <path d=\"M 42.620313 832.218125 \n",
       "L 42.620313 717.078125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_24\">\n",
       "    <path d=\"M 694.779688 832.218125 \n",
       "L 694.779688 717.078125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_25\">\n",
       "    <path d=\"M 42.620313 832.218125 \n",
       "L 694.779688 832.218125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_26\">\n",
       "    <path d=\"M 42.620313 717.078125 \n",
       "L 694.779688 717.078125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_65\">\n",
       "    <!-- Sample Function 4 -->\n",
       "    <g transform=\"translate(312.7275 711.078125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-83\"/>\n",
       "     <use x=\"63.476562\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"124.755859\" xlink:href=\"#DejaVuSans-109\"/>\n",
       "     <use x=\"222.167969\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "     <use x=\"285.644531\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "     <use x=\"313.427734\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"374.951172\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"406.738281\" xlink:href=\"#DejaVuSans-70\"/>\n",
       "     <use x=\"464.179688\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "     <use x=\"527.558594\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"590.9375\" xlink:href=\"#DejaVuSans-99\"/>\n",
       "     <use x=\"645.917969\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "     <use x=\"685.126953\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "     <use x=\"712.910156\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "     <use x=\"774.091797\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "     <use x=\"837.470703\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"869.257812\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p288a196540\">\n",
       "   <rect height=\"115.14\" width=\"652.159375\" x=\"42.620313\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pfdf341ae17\">\n",
       "   <rect height=\"115.14\" width=\"652.159375\" x=\"42.620313\" y=\"196.008125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p23674a6dd6\">\n",
       "   <rect height=\"115.14\" width=\"652.159375\" x=\"42.620313\" y=\"369.698125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p1fa8443931\">\n",
       "   <rect height=\"115.14\" width=\"652.159375\" x=\"42.620313\" y=\"543.388125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pbfebe2a693\">\n",
       "   <rect height=\"115.14\" width=\"652.159375\" x=\"42.620313\" y=\"717.078125\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x1152 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "N = 5  # number of sample functions\n",
    "\n",
    "# draw N sample functions from a random process\n",
    "np.random.seed(0)\n",
    "x = np.random.normal(size=(N, 32))\n",
    "\n",
    "# plot sample functions\n",
    "fig = plt.figure(figsize=(10, 12))\n",
    "for n in range(N):\n",
    "    plt.subplot(N, 1, n+1)\n",
    "    plt.tight_layout()\n",
    "    plt.stem(x[n, :], basefmt='C0:', use_line_collection=True)\n",
    "    plt.title('Sample Function %d' % n)\n",
    "    plt.xlabel(r'$k$')\n",
    "    plt.ylabel(r'$x_%d[k]$' % n)\n",
    "    plt.axis([-1, 32, -3, 3])\n",
    "    plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* What is different, what is common between the sample functions?\n",
    "\n",
    "Solution: You may have observed that the amplitude values of the individual sample functions $x_n[k]$ differ for a fixed time instant $k$. However, the sample functions seem to share some common properties. For instance, positive and negative values seem to occur with approximately the same probability. Furthermore, positive and negative values seem to be aligned around zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties of Random Processes and Random Signals\n",
    "\n",
    "It was already argued above, that it is not meaningful to describe a random signal by the amplitude values of a particular sample function. Instead, random signals are characterized by specific statistical measures. In statistical signal processing it is common to use\n",
    "\n",
    "* amplitude distributions and\n",
    "* ensemble averages/moments\n",
    "\n",
    "for this purpose. These measures will be introduced in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
